Solving this integral with u substitution

[karush]

Homework Statement

u subst

Relevant Equations

u subst

Evaluate $\displaystyle\int_{0}^{3}\frac{x+3}{\sqrt{x^{3}+1}}dx+5$
W|A returned 11.7101
ok subst is probably just one way to solve this so
$u=x^{3}+1 \quad du= 3x^2$

 

[malawi_glenn]

What did you try? what is w|A?

 

[karush]

Wolffram Alpha
u subst

 

[Orodruin]

Please show your work

 

[karush]

Please show your work

I did what I could in the OP

 

[Orodruin]

You did nothing in the OP apart from just stating a substitution. What does that give you? Where do you get stuck? Please be specific.

 

[karush]

ok I can't see how this subst would play out
or do I need to go somewhere elae for help
$$u=x^3+1\quad du=3x^2 \quad (u-1)^{1/3}=x$$
this doesn't render

 

[berkeman]

this doesn't render

It does render properly now that I changed your single-$ delimiters to double-$ delimiters.

or do I need to go somewhere elae for help

If you expect us to do your work for you without you showing any effort, then yes. If you are willing to put in some effort, then you will get great help here at PF.

 

[Mark44]

I don't think an ordinary substitution by itself will do the trick. Something to try is 1) the substitution $u = x^{3/2}$, followed by 2) a trig substitution. The first substitution turns the denominator to $\sqrt{u^2 + 1}$, which suggests a trig substitution. I worked it through part way, but didn't complete my work, so I'm not sure that this will bear fruit.

 

[karush]

It does render properly now that I changed your single-$ delimiters to double-$ delimiters. If you expect us to do your work for you without you showing any effort, then yes. If you are willing to put in some effort, then you will get great help here at PF.

sorry there is a typo in the OP it should be $x^2$ not $x^3$

i have already solved the problem by expansion

 

[SammyS]

sorry there is a typo in the OP it should be $x^2$ not $x^3$

i have already solved the problem by expansion

So this means that the OP should read:

Homework Statement: Evaluate $\displaystyle\int_{0}^{3}\frac{x+3}{\sqrt{x^{2}+1}}dx+5$

Relevant Equations: u subst

ok subst is probably just one way to solve this so

The indefinite integral, $\displaystyle \int \frac{x+3}{\sqrt{x^{2}+1}}dx$, does have a closed form solution,

Break that into the sum of integrals: $\displaystyle \int \frac{x}{\sqrt{x^{2}+1}}dx + 3\int \frac{1}{\sqrt{x^{2}+1}}dx$ .

The first can be handled by a relatively simple substitution.

The second can be done with:
1) a trig substitution, the result of which may require knowing $\int \sec \theta \ d\theta$.

2) a hyperbolic function substitution .

3) knowledge of the derivative of the inverse hyperbolic sine function.

 

[karush]

Mahalo every one